We've had months of warning about the June 1st deadline. There have been radio announcements about the importance of renewing our passports for at least the past 6 months. And the border guards have been preparing for this.

I wouldn't take the chance for a bicycle ride. I don't think you'd end up with cavity searches or anything like that ... but I do think you'd end up with a hefty fine, and it would likely be a lot of years before you'd be allowed back in Canada again, and you'd have a note on your information that will follow you and create suspicion if you ever try to go to another country again.